This paper is concerned with the parameter estimation of a relatively general class of nonlinear dynamic systems. A Maximum Likelihood (ML) framework is employed in the interests of statistical efficiency, and it is illustrated how an Expectation Maximisation (EM) algorithm may be used to compute these ML estimates. An essential ingredient is the employment of so-called ``particle smoothing'' methods to compute required conditional expectations via a Monte Carlo approach. A simulation example demonstrates the efficacy of these techniques.